The city Department of Education lost track of a number of employees who had quietly stopped reporting to work for as long as a year — but continued to pay their hefty salaries anyway, agency documents reveal.

Those who “disappeared” include a teacher who requested leave but was turned down, a school psychologist who simply stopped reporting to assignments as a substitute, and a school aide who took three extended leaves for the same injury.

The stunning failure in basic housekeeping — which was uncovered by several external investigations — went on for at least a year despite pleas by the special schools investigator that the DOE address the lapse in personnel protocol, documents show.

“It is a recurring problem that DOE employees disappear from assignments for long periods of time but continue to get paid,” a report by Special Commissioner of Investigation Richard Condon concluded in March 2011. “No one accepts responsibility for the mistake.”

Despite his request that officials respond with a written protocol for tracking employees, none had been provided as of earlier this year.

“The problem continues, and the DOE has not reported a plan to correct it,” Condon wrote after a separate probe in February 2012.

A spokeswoman for his office would not comment on whether the protocol has been supplied since.

Among the AWOL employees busted for collecting unmerited paychecks was former Queens school psychologist Janet Strobel, who admitted that she “just stopped going to work” for a year because of emotional distress — but still netted $108,000, according to a report.

One of her supervisors claimed Strobel, who was working as a long-term substitute at the time, had mentioned retiring, while another said she had refused an assignment at a high school in Long Island City.

Yet neither could explain why Strobel’s former school, PS 37 in Jamaica, continued to issue her checks for the entire 2008-09 school year despite the fact that she no longer worked there.

When asked by The Post why she accepted payment when she hadn’t been working, she said, “That’s none of your business.”

Other no-shows outed by Condon include:

* Manhattan teacher Maegan Henriquez-Ford, who went on sick and injury leave for a whopping two years, but whose request to do so had been denied. She was paid $115,000 from Dec. 2009 through Sept. 2011 without working a day.

* Bronx aide Rita Anderson went out for the same line-of-duty injury to her wrist three times in five years, taking time off for at least 1.5 years. She was overpaid more than $31,000.

Department of Education spokeswoman Connie Pankratz called the no-show payments “unique situations” that were immediately corrected, explaining that the agency has protocols in place to track its workers — and that all three educators have been terminated.

“Now, anyone who does not show up for an assignment is immediately reported for further investigation,” said Pankratz.